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Zhaqilao; Li, Zhi-Bin

Darboux transformation and various solutions for a nonlinear evolution equation in \((3+1)\)-dimensions. (English) Zbl 1175.35132

Mod. Phys. Lett. B 22, No. 30, 2945-2966 (2008).
Summary: A new \((3+1)\)-dimensional nonlinear evolution equation can be decomposed into three \((1+1)\)-dimensional nonlinear evolution equations. In this paper, \(N\)-soliton solution, resonant solution and complexiton solution of the \((3+1)\)-dimensional nonlinear evolution equation are obtained via an \(N\)-fold Darboux transformation of the Ablowitz-Kaup-Newell-Segur spectral problems.

Cited in 7 Documents

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35Q51 Soliton equations
37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
37K35 Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems
35C05 Solutions to PDEs in closed form

Keywords:

soliton solution; Darboux transformation; nonlinear evolution equation
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References:

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